CHAPTER 12 PART B– INVENTORY MANAGEMENT Suman Niranjan

QUANTITY DISCOUNTS

Annualcarryingcost

PurchasingcostTC = +

Q2H D

QSTC = +

+Annualorderingcost

PD + 2

TOTAL COSTS WITH PD

Cost

EOQ

TC with PD

TC without PD

PD

0 Quantity

Adding Purchasing costdoesn’t change EOQ

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TOTAL COST WITH QUANTITY DISCOUNTS

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CARRYING COSTS

Two types of carrying costs Fixed or constant per unit Specified as a fixed percentage of unit price

Determining best purchase quantity when carrying costs are constant1. Compute the minimum order quantity (EOQ)2. Only one unit price will have the EOQ in feasible

rangea) If the feasible EOQ is on the lowest price range, that is

the optimal order quantity.b) If the feasible EOQ is in any other range, compute the

total cost for the EOQ and for the price breaks of all lower unit costs. Compare the total costs; the quantity (minimum point or price break) that yields the lowest total cost is the optimal order quantity.

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EXAMPLE 5

The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost.

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CARRYING COSTS

When carrying costs are expressed as a percentage of unit price, determine the best purchase quantity:1. Beginning with the lowest unit price, compute

the EOQ for each price range until you find a feasible minimum point (i.e., until a minimum point falls in the quantity range for its price).

2. If the minimum point for the lowest unit price is feasible, it is the optimal order quantity. If the minimum point is not feasible in the lowest price range, compare the total cost at the price break for all lower prices with the total cost of the feasible minimum point. The quantity that yields the lowest total cost is the optimum.

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EXAMPLE 6

Surge Electric uses 4,000 toggle switches a year. Switches are priced as follows: 1 to 499, 90 cents each; 500 to 999, 85 cents each; and 1,000 or more, 80 cents each. It costs approximately $30 to prepare an order and receive it, and carrying costs are 40 percent of purchase price per unit on an annual basis. Determine the optimal order quantity and the total annual cost.

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OVERVIEW

When to reorder with EOQ Shortages and service levels

Fill Rate How much to order

Fixed quantity-interval model The single period model

Newsboy model

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WHEN TO REORDER WITH EOQ ORDERING Reorder Point - When the quantity on hand of

an item drops to this amount, the item is reordered

Safety Stock - Stock that is held in excess of expected demand due to variable demand rate and/or lead time.

Service Level - Probability that demand will not exceed supply during lead time. (the amount of stock on-hand will be able to meet the demand) Example:

95% service level10

DETERMINANTS OF THE REORDER POINT The rate of demand The lead time Demand and/or lead time variability Stockout risk (safety stock)

Example 6 Tingly takes Two-a-Day vitamins, which are

delivered to his home by a routeman seven days after an order is called in. At what point should Tingly reorder?

If demandand lead timeareconstant:

ROP =d*LT

d = Demand rate unitsper dayor week

LT = Lead timein daysor weeks

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ROP

When variability is present in the demand: Actual demand will exceed the expected demand Carry additional stock known as Safety Stock

ROP = Expected Demand During Lead Time + Safety Stock

Service level = 100 percent – stockout risk

ROP Expected Demand During Lead Time +z dLT

Safety Stock z dLT

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SAFETY STOCK

LT Time

Expected demandduring lead time

Maximum probable demandduring lead time

ROP

Qu

an

tity

Safety stock

Safety stock reduces risk ofstockout during lead time

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REORDER POINT

ROP

Risk ofa stockout

Service level

Probability ofno stockout

Expecteddemand Safety

stock0 z

Quantity

z-scale

The ROP based on a normalDistribution of lead time demand

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EXAMPLE 8

Suppose that the manager of a construction supply house determined from historical records that demand for sand during lead time averages 50 tons. In addition, suppose the manager determined that demand during lead time could be described by a normal distribution that has a mean of 50 tons and a standard deviation of 5 tons. Answer these questions, assuming that the manager is willing to accept a stockout risk of no more than 3 percent: What value of z is appropriate? How much safety stock should be held? What reorder point should be used?

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CASES OF ROP

When data on demand during lead time is not available Using the available data we can find if the

demand and/or lead time is random If only demand is random

If only lead time is random

If demand and lead time is random

* dROP d LT z LT

* LTROP d LT zd

2 2 2* * d LTROP d LT z LT d 16

EXAMPLE 9

A restaurant uses an average of 50 jars of a special sauce each week. Weekly usage of sauce has a standard deviation of 3 jars. The manager is willing to accept no more than a 10 percent risk of stockout during lead time, which is two weeks. Assume the distribution of usage is normal. Which of the above formulas is appropriate for

this situation? Why? Determine the value of z. Determine the ROP.

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FIXED-ORDER-INTERVAL MODEL

Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory

levels Risk of stockout Fill rate – the percentage of demand filled by

the stock on hand

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Fixed Order

Fixed Interval

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